Answer:
tan A = - [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
Using the identity sin² A + cos² A = 1, then
([tex]\frac{4}{5}[/tex] )² + cos² A = 1
[tex]\frac{16}{25}[/tex] + cos² A = 1 ( subtract [tex]\frac{16}{25}[/tex] from both sides )
cos² A = [tex]\frac{9}{25}[/tex] ( take the square root of both sides )
cos A = ± [tex]\sqrt{\frac{9}{25} }[/tex] and given cosA < 0, then
cos A = - [tex]\frac{3}{5}[/tex]
Using the identity
tan A = [tex]\frac{sinA}{cosA}[/tex], then
tan A = [tex]\frac{\frac{4}{5} }{-\frac{3}{5} }[/tex] = [tex]\frac{4}{5}[/tex] × - [tex]\frac{5}{3}[/tex] = - [tex]\frac{4}{3}[/tex]
